The periodontal probing should not hurt. Unless you’re seeing a periodontist, the hygienist usually does the probing. If the hygienist is inexperienced, s/he may not have learned to do a fairly painless exam yet. The perio probe should gently follow the tooth surface until it stops. It should never be pushed or twisted as that can damage the attachment of the tissue to the root. Your experience is not normal.
A bleeding gum will not show on an xray. You would possibly see bone loss, depending on the area that has a higher number on the probe. Did the dentist say you have bleeding on probing, and what was the number? And yes, you can have a pocket develop without any symptoms noticed by you. 4 months is very quick, but a 3 to a 4 can happen in that time frame. Do you have the same hygienist for every appointment?
Did the dentist give you a diagnosis and treatment plan, and what was it? Let’s start here.